Sur une inégalité de H. P. Rosenthal et le théorème limite central dans les espaces de Banach
type: Item
instance of: scholarly article
title: Sur une inégalité de H. P. Rosenthal et le théorème limite central dans les espaces de Banach
zbMATH Open document ID: 0576.60009
DOI: 10.1007/BF02759762
author: Michel Ledoux
published in: Israel Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The author uses the \textit{J. Zinn} [see Probability in Banach spaces III, Proc. 3rd int. Conf., Medford/USA 1980, Lect. Notes Math. 860, 324-329 (1981; Zbl 0482.60009)] reformulation of the \textit{H. P. Rosenthal} [ibid. 8, 273-303 (1970; Zbl 0213.193) and Proc. 6th Berkeley Sympos. math. Statist. Probab., Univ. Calif. 1970, 2, 149-167 (1972; Zbl 0255.60003)] generalisation of Khintchine inequalities to study the central limit theorem in Banach spaces. He proves that the validity of the Rosenthal- Zinn inequality characterizes the spaces for which the classical necessary conditions to the CLT are also sufficient ones.
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 3921604
zbMATH Keywords: Khintchine inequalities
zbMATH Keywords: central limit theorem in Banach spaces
zbMATH Keywords: Rosenthal-Zinn inequality
reviewed by: Jean-Thierry Lapresté
MaRDI profile type: Publication
cites work: The Integral of a Symmetric Unimodal Function over a Symmetric Convex Set and Some Probability Inequalities
cites work: Q3906818
cites work: Gaussian characterizations of certain Banach spaces
cites work: Q4167324
cites work: Q5606327
cites work: Q3858986
cites work: Central limit theorems and weak laws of large numbers in certain banach spaces
cites work: On the law of large numbers in 2-uniformly smooth Banach spaces
cites work: Sums of independent Banach space valued random variables
cites work: The law of large numbers and the central limit theorem in Banach spaces
cites work: Q4171332
cites work: Q5587572
cites work: Q4048075
cites work: Some stability results for vector valued random variables
cites work: Q5623005
cites work: Q5639057
cites work: Q3042065
cites work: Q4188284
cites work: Q4084217
cites work: Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach
cites work: Q4776391
cites work: Q4054229
cites work: Q4188489
cites work: On the Dimension of the l n p -Subspaces of Banach Spaces, for 1 p < 2
cites work: On the limit theorems for random variables with values in the spaces L p (2?p<?)
cites work: On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
cites work: Q5670003
cites work: Q4748883
cites work: Q3968218
cites work: Q3940543
description: scientific article; zbMATH DE number 3921604